Reactor models, applications model

That is, instead of determining the transport properties from the rather theoretical Enskog solution of the Boltzmann equation, for practical applications we may often resort to the much simpler but still fairly accurate mean free path approach (e.g., [12], section 5.1 [87], chap. 20 [34], section 9.6). Actually, the form of the relations resulting from the mean free path concept are about the same as those obtained from the much more complex theories, and even the values of the prefactors are considered sufficiently accurate for many reactor modeling applications. 

There is a general trend toward structured packings and monoliths, particularly in demanding applications such as automotive catalytic converters. In principle, the steady-state performance of such reactors can be modeled using Equations (9.1) and (9.3). However, the parameter estimates in Figures 9.1 and 9.2 and Equations (9.6)-(9.7) were developed for random packings, and even the boundary condition of Equation (9.4) may be inappropriate for monoliths or structured packings. Also, at least for automotive catalytic converters. 

The two BCs of the TAP reactor model (1) the reactor inlet BC of the idealization of the pulse input to tiie delta function and (2) the assumption of an infinitely large pumping speed at the reactor outlet BC, are discussed. Gleaves et al. [1] first gave a TAP reactor model for extracting rate parameters, which was extended by Zou et al. [6] and Constales et al. [7]. The reactor equation used here is an equivalent form fi om Wang et al. [8] that is written to be also applicable to reactors with a variable cross-sectional area and diffusivity. The reactor model is based on Knudsen flow in a tube, and the reactor equation is the diffusion equation ... 

Beltran FJ, Gonzalez M, Rivas FJ, et al. 1995. Application of photochemical reactor models to UV irradiation of trichloroethylene in water. Chemosphere 31 2873-2885. 

Hamielec, A.E., Computer Applications Modeling of Polymer Reactor Systems , Proceedings - Polymer Characterization Conference, Cleveland State University. Division of Continuing Mucation, Qeveland, Ohio, April 30 - May 1, 1974. 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

Other Monomer Systems. Very slight modifications are required to make the model applicable to emulsion homopolymerization of vinyl chloride (VCM). An initial study on PVC reactors has been reported in (69) and some more recent results following will finely illustrate the case. 

The bread and butter tools of the practicing chemical engineer are the material balance and the energy balance. In many respects chemical reactor design can be regarded as a straightforward application of these fundamental principles. This section indicates in general terms how these principles are applied to the various types of idealized reactor models. 

We can characterize the mixed systems most easily in terms of the longitudinal dispersion model or in terms of the cascade of stirred tank reactors model. The maximum amount of mixing occurs for the cases where Q)L = oo or n = 1. In general, for reaction orders greater than unity, these models place a lower limit on the conversion that will be obtained in an actual reactor. The applications of these models are treated in Sections 11.2.2 and 11.2.3. 

The application of CFD to packed bed reactor modeling has usually involved the replacement of the actual packing structure with an effective continuum (Kvamsdal et al., 1999 Pedernera et al., 2003). Transport processes are then represented by lumped parameters for dispersion and heat transfer (Jakobsen... 

Many wastewater flows in industry can not be treated by standard aerobic or anaerobic treatment methods due to the presence of relatively low concentration of toxic pollutants. Ozone can be used as a pretreatment step for the selective oxidation of these toxic pollutants. Due to the high costs of ozone it is important to minimise the loss of ozone due to reaction of ozone with non-toxic easily biodegradable compounds, ozone decay and discharge of ozone with the effluent from the ozone reactor. By means of a mathematical model, set up for a plug flow reactor and a continuos flow stirred tank reactor, it is possible to calculate more quantitatively the efficiency of the ozone use, independent of reaction kinetics, mass transfer rates of ozone and reactor type. The model predicts that the oxidation process is most efficiently realised by application of a plug flow reactor instead of a continuous flow stirred tank reactor. 

The IWA (International Water Association), formerly known as the IWQA, has had several task forces working on model development for various types of processes. I believe that these reactor models have a good potential application for remedial treatment. The subject of the models is extremely complex and too involved for this discussion, as it is a Master s Level course in Environmental Engineering. However, let me indicate that there are several types of models which may have some application to the bioremediation field. The principal models are... 

Arthur D. Little has carried out cost structure studies for a variety of fuel cell technologies for a wide range of applications, including SOFC tubular, planar and PEM technologies. Because phenomena at many levels of abstraction have a significant impact on performance and cost, they have developed a multi-level system performance and cost modeling approach (see Figure 1-15). At the most elementary level, it includes fundamental chemical reachon/reactor models for the fuel processor and fuel cell as one-dimensional systems. 

To facilitate the design and application of the nonlinear robust control law, let us rewrite the pol3unerization reactor modeling equations (42) in the state space ... 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Using these methods, the elementary reaction steps that define a fuel s overall combustion can be compiled, generating an overall combustion mechanism. Combustion simulation software, like CHEMKIN, takes as input a fuel s combustion mechanism and other system parameters, along with a reactor model, and simulates a complex combustion environment (Fig. 4). For instance, one of CHEMKIN s applications can simulate the behavior of a flame in a given fuel, providing a wealth of information about flame speed, key intermediates, and dominant reactions. Computational fluid dynamics can be combined with detailed chemical kinetic models to also be able to simulate turbulent flames and macroscopic combustion environments. 

The skew in the fit of the tracer curve in Example 6.7 occurs because the tails are not modeled well. This is a problem with the reactors-in-series model and most computational models as well. A solution to this curve-fit problem will be discussed in the next section on leaky dead zones. For most applications, in transport modeling. 

We have chosen to concentrate on a specific system throughout the chapter, the methanation reaction system. Thus, although our development is intended to be generally applicable to packed bed reactor modeling, all numerical results will be obtained for the methanation system. As a result, some approximations that we will find to apply in the methanation system may not in other reaction systems, and, where possible, we will point this out. The methanation system was chosen in part due to its industrial importance, to the existence of multiple reactions, and to its high exothermicity. 

A significant step in the numerical solution of packed bed reactor models was taken with the introduction of the method of orthogonal collocation to this class of problems (Finlayson, 1971). Although Finlayson showed the method to be much faster and more accurate than that based on finite differences and to be easily applicable to two-dimensional models with both radial temperature and concentration gradients, the finite difference technique remained the generally accepted procedure for packed bed reactor model solution until about 1977, when the analysis by Jutan et al. (1977) of a complex butane hydrogenolysis reactor demonstrated the real potential of the collocation procedure. 

In this case, the model equations derived for the slurry bubble column reactor are applicable. Note that if the gas-phase concentration is constant, the gas-phase material balance is not needed (where the two reactors have different model equations). 

Model application in the trickle-flow regime In order to assure operation in the trickle-flow regime, the gas as well as the liquid flow rate has to be considerably lowered. At the same time, the conditions (a) and (d) are met in the reactor, while the rest of the conditions have to be checked. 

A brief review of the development history of monolith reactor models for TWC applications can be found in Koltsakis and Stamatelos (1997). Various workers have looked at 1-, 2- and 3-dimensional models considering both the whole monolith and just a single channel. A multidimensional model for the whole monolith is required for investigating the effects of a flow maldistribution across the front face of the monolith, but is probably unnecessary when the flow is uniform. Other workers have studied multidimensional single channel models, where the gas flow within the channel is modelled in detail. In general, for a model to be useful in practice, some compromise has to be made between having a reasonable runtime versus detail/complexity, both in terms of the chemical kinetics and the description of the flow field within the channels of and across the monolith. 

The catalyst and particulate filter models were developed individually with different university partners. They are described in the following sections. A key issue for all models is robustness and scalability as the applications range from passenger cars to heavy-duty commercial vehicles. The models are physical and chemically based, consisting of a transport model for heat and mass transfer phenomena in the monolith in gas and solid phases, cf. Fig. 6. The monolith reactor modeling is discussed in more detail in Section III. 

Well over 50 large-scale EO model-based RTO applications have been deployed for petroleum refining processes. These model applications have been deployed in petroleum refineries Liporace et al., 2009 Camolesi et al., 2008 Mudt et al., 1995, both on separation units (crude atmospheric and vacuum distillation units) and on reactor units (including fluidized catalytic crackers (FCC), gasoline reformers, and hydrocrackers). 

As a more critical example concerning the transfer of macroscopic modeling to micro-scale applications, the following example of a simulation of a homogeneous catalytic reaction is described [133], This example also represents a typical approach in process simulation if a new reactor model or a model for a new unit operation... 

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